Russian Journal of Electrochemistry

, Volume 54, Issue 11, pp 783–795 | Cite as

Kinetic Mechanism for Modelling of Electrochemical Mediatedenzyme Reactions and Determination of Enzyme Kinetics Parameters

  • O. M. KirthigaEmail author
  • L. Rajendran
  • Carlos Fernandez


The non-steady state current density for reversible electrochemical coupled with a homogeneous enzyme reaction and a constant potential is presented in this manuscript for the first time. The model is based on non-stationary diffusion equations with semi infinite boundary condition containing a nonlinear term related to the kinetics of an enzymatic reaction. The nonlinear differential equation for the mediator is solved for reversible homogeneous enzyme reaction. Approximate analytical expressions for the concentration of the mediator and corresponding current for non-steady state conditions are derived. Kinetic parameters are also determined such as Michaelis–Menten constants for substrate (KMS) and mediator (KMM) as well as catalytic rate constant (kcat). Upon comparison, we found that the analytical results of this work are in excellent agreement with the numerical (Matlab program) and existing limiting case results. The significance of the analytical results has been demonstrated by suggesting two new graphical procedures for estimating the kinetic parameters from the current densities.


mathematical modelling non-linear reaction diffusion equations enzyme electrode mediated enzyme reactions 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Nicholson, R.S. and Shain, I., Theory of stationary electrode polarography. single scan and cyclic methods applied to reversible, irreversible, and kinetic systems, Anal. Chem., 1964, vol. 36, p. 706.CrossRefGoogle Scholar
  2. 2.
    Leypoldt, J.K. and Gough, D.A., Model of a two-substrate enzyme electrode for glucose, Anal. Chem., 1984, vol. 56, p. 2896.CrossRefGoogle Scholar
  3. 3.
    Bartlett, P.N. and Whitaker, R.G., Electrochemical immobilisation of enzymes. Part I. Theory, J. Electroanal. Chem., 1987, vol. 224, p. 27.CrossRefGoogle Scholar
  4. 4.
    Bartlett, P.N. and Whitaker, R.G., Electrochemical immobilisation of enzymes. Part II. Glucose oxidase immobilised in poly-n-methylpyrrole, J. Electroanal. Chem., 1987, vol. 224, p. 37.CrossRefGoogle Scholar
  5. 5.
    Rusling, J.F. and Ito, K., Voltammetric determination of electron-transfer rate between an enzyme and a mediator, Anal. Chim. Acta, 1991, vol. 252, p. 23.CrossRefGoogle Scholar
  6. 6.
    Bartlett, P.N. and Pratt, K.F.E., Modeling of processes in enzyme electrodes, Biosens. Bioelectron., 1993, vol. 8, p. 451.CrossRefGoogle Scholar
  7. 7.
    Britz, D., Digital Simulation in Electrochemistry, 2nd ed., Berlin: Springer-Verlag, 1988.CrossRefGoogle Scholar
  8. 8.
    Mell, L.D. and Maloy, J.T., A model for the amperometric enzyme electrode obtained through digital simulation and applied to the immobilized glucose oxidase system, Anal. Chem., 1975, vol. 47, p. 299.CrossRefGoogle Scholar
  9. 9.
    Bergel, A. and Comtat, M., Theoretical evaluation of transient responses of an amperometric enzyme electrode, Anal. Chem., 1984, vol. 56, p. 2904.CrossRefGoogle Scholar
  10. 10.
    Lucisano, J.Y. and Gough, D.A., Transient response of the two-dimensional glucose sensor, Anal. Chem., 1988, vol. 60, p. 1272.CrossRefGoogle Scholar
  11. 11.
    Battaglini, F. and Calvo, E.J., Digital-simulation of homogeneous enzyme-kinetics for amperometric redox-enzyme electrodes, Anal. Chim. Acta, 1992, vol. 258, p. 151.CrossRefGoogle Scholar
  12. 12.
    Martens, N. and Hall, E.A.H., Model for an immobilized oxidase enzyme electrode in the presence of two oxidants, Anal. Chem., 1994, vol. 66, p. 2763.CrossRefGoogle Scholar
  13. 13.
    Osman, M.H., Shah, A.A., Wills, R.G.A., and Walsh, F.C., Mathematical modelling of an enzymatic fuel cell with an air-breathing cathode, Electrochim. Acta, 2013, vol. 112, p. 386.CrossRefGoogle Scholar
  14. 14.
    Do, T.Q.N., Varničić, M., Hanke-Rauschenbach, R., Vidaković-Koch, T., and Sundmacher, K., Mathematical modeling of a porous enzymatic electrode with direct electron transfer mechanism, Electrochim. Acta, 2014, vol. 137, p. 616.CrossRefGoogle Scholar
  15. 15.
    Picioreanu, C., Head, I.M., Katuri, K.P., van Loosdrecht, M.C.M., and Scott, K., A computational model for biofilm-based microbial fuel cells, Water Res., 2007, vol. 41, p. 2921.CrossRefGoogle Scholar
  16. 16.
    Eswari, A. and Rajendran, L., Mathematical modeling of cyclic voltammetry for ec reaction, Russ. J Electrochem., 2011, vol. 47, p. 181.CrossRefGoogle Scholar
  17. 17.
    Eswari, A. and Rajendran, L., Mathematical modeling of cyclic voltammetry for ec2 reaction, Russ. J Electrochem., 2011, vol. 47, p. 191.CrossRefGoogle Scholar
  18. 18.
    Eloul, S. and Compton, R.G., Voltammetric sensitivity enhancement by using preconcentration adjacent to the electrode: simulation, critical evaluation, and insights, J. Phys. Chem. C, 2014, vol. 118, p. 24520.CrossRefGoogle Scholar
  19. 19.
    Molina, A., Serna, C., Li, Q., Laborda, E., Batchelor-McAuley, C., and Compton, R.G., Analytical solutions for the study of multielectron transfer processes by staircase, cyclic, and differential voltammetries at disc microelectrodes, J. Phys. Chem. C, 2012, vol. 116, p. 11470.Google Scholar
  20. 20.
    Kenji, Y., Satoshi, K., and Yoshihiro, K., Cyclic Voltammetric simulation of electrochemically mediated enzyme reaction and elucidation of biosensor behaviors, Anal. Bioanal. Chem., 2002, vol. 372, p. 248.CrossRefGoogle Scholar
  21. 21.
    Rajendran, L. and Saravankumar, K., Analytical expression of transient and steady-state catalytic current of mediated bioelectrocatalysis, Electrochim. Acta, 2014, vol. 147, p. 678.CrossRefGoogle Scholar
  22. 22.
    Kenji, Y. and Yoshihiro, K., Cyclic voltammetric simulation for electrochemically mediated enzyme reaction and determination of enzyme kinetic constants, Anal. Chem., 1998, vol. 70, p. 3368.CrossRefGoogle Scholar
  23. 23.
    He, J.H. and Mo, L.F., Comments on “Analytical solution of amperometric enzymatic reactions based on homotopy perturbation method,” Electrochim. Acta, 2013, vol. 102, p. 472.Google Scholar
  24. 24.
    Rajendran, L. and Anitha, S., Reply to “Comments on analytical solution of amperometric enzymatic reactions based on homotopy perturbation method,” by Ji-Huan He, Lu-Feng Mo, Electrochim. Acta, 2013, vol. 102, p. 474.CrossRefGoogle Scholar
  25. 25.
    Kirthiga, O.M. and Rajendran, L., Approximate analytical solution for non-linear reaction diffusion equations in a mono-enzymatic biosensor involving michaelis–menten kinetics, J. Electroanal. Chem., 2015, vol. 751, p. 119.CrossRefGoogle Scholar
  26. 26.
    Danckwerts, P.V., Absorption by simultaneous diffusion and chemical reaction into particles of various shapes and into falling drops, Trans Faraday Soc., 1951, vol. 47, p. 1014.CrossRefGoogle Scholar
  27. 27.
    Rahamathunissa, G., Basha, C.A., and Rajendran, L., The theory of reaction-diffusion processes at cylindrical ultramicroelectrodes, J. Theor. Comput. Chem., 2007, vol. 6, p. 301.CrossRefGoogle Scholar
  28. 28.
    Rasi, M., Rajendran, L., and Sangaranarayanan, M.V., Enzyme-catalyzed oxygen reduction reaction in biofuel cells: Analytical expressions for chronoamperometric current densities, J. Electrochem. Soc., 2015, vol. 162, p. H671.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • O. M. Kirthiga
    • 1
    Email author
  • L. Rajendran
    • 1
  • Carlos Fernandez
    • 2
  1. 1.Department of MathematicsSethu Institute of TechnologyKariapattiIndia
  2. 2.Department of Analytical Chemistry, School of Pharmacy and Life SciencesRobert Gordon UniversityAberdeenUK

Personalised recommendations